Frontiers of Mathematics in China >
von Neumann’s mean ergodic theorem on complete random inner product modules
Received date: 29 Jan 2011
Accepted date: 14 Apr 2011
Published date: 01 Oct 2011
Copyright
We first prove two forms of von Neumann’s mean ergodic theorems under the framework of complete random inner product modules. As applications, we obtain two conditional mean ergodic convergence theorems for random isometric operators which are defined on and generated by measure-preserving transformations on Ω, where H is a Hilbert space, (1≤p<∞) the Banach space of equivalence classes of H-valued p-integrable random variables defined on a probability space (Ω, , P), a sub σ-algebra of , and the complete random normed module generated by .
Xia ZHANG , Tiexin GUO . von Neumann’s mean ergodic theorem on complete random inner product modules[J]. Frontiers of Mathematics in China, 2011 , 6(5) : 965 -985 . DOI: 10.1007/s11464-011-0139-4
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